The increasing deployment of Large Vision-Language Models (LVLMs) raises safety concerns under potential malicious inputs. However, existing multimodal safety evaluations primarily focus on model vulnerabilities exposed by static image inputs, ignoring the temporal dynamics of video that may induce distinct safety risks. To bridge this gap, we introduce Video-SafetyBench, the first comprehensive benchmark designed to evaluate the safety of LVLMs under video-text attacks. It comprises 2,264 video-text pairs spanning 48 fine-grained unsafe categories, each pairing a synthesized video with either a harmful query, which contains explicit malice, or a benign query, which appears harmless but triggers harmful behavior when interpreted alongside the video. To generate semantically accurate videos for safety evaluation, we design a controllable pipeline that decomposes video semantics into subject images (what is shown) and motion text (how it moves), which jointly guide the synthesis of query-relevant videos. To effectively evaluate uncertain or borderline harmful outputs, we propose RJScore, a novel LLM-based metric that incorporates the confidence of judge models and human-aligned decision threshold calibration. Extensive experiments show that benign-query video composition achieves average attack success rates of 67.2%, revealing consistent vulnerabilities to video-induced attacks. We believe Video-SafetyBench will catalyze future research into video-based safety evaluation and defense strategies.